The present invention relates to a signal processing unit for forming frequency spectrum by utilizing, for instance, nuclear magnetic resonance. More particularly, it relates to a signal processing unit for forming frequency spectrum by calibrating errors automatically.
For forming frequency spectrum by utilizing nuclear magnetic resonance without using any error-calibrating function, adjustment should be made as to an unit as follows. Namely, two reference signals having adjusted phase difference of 90.degree. are respectively fed into two sensitive phase detectors, each having the same output signal, to carry out synchronous detection thereby outputting absorption components and dispersion components. In this case, there possibly takes place omission of signals because amplifiers have their inherent insensitive time. It is, therefore, necessary to carry out synchronous detection by producing an echo signal to prevent omission of the signals. The frequency spectrum is formed by subjecting detected outputs to signal processing in a computer device. When the detected signals are converted into a digital form in the computer device, each center of both the absorption components and the dispersion components of the echo signal should be in a digital form. In this case, control of meters and devices have to be made so as not to take place variations of the echo signal due to ageing of the amplifiers and the sensitive phase detectors whereby a signal at the front half portion or at the rear half portion with respect to the center of the echo signal is used for spectrum analysis. However, it is difficult either to perform phase adjustment of the reference signals so as to produce the absorption components and dispersion components from an output of the sensitive phase detector or to eliminate change in characteristic of the meters and devices due to the ageing of them. Further, it is also difficult to contrive so that the center of the echo signal has a digital value, on account of which there takes place difficulty in using a half portion of the signal with respect to the center of the echo signal for performing the spectrum analysis. This results in an error of frequency spectrum and it is, therefore, necessary to calibrate the error.
The operation of the conventional signal processing unit to perform calibration of errors will be described with reference to FIGS. 1 and 2.
FIG. 1 is a block diagram showing a construction of the conventional system.
The conventional signal processing unit comprises an amplifier 2 for amplifying a signal received by a receiver 1, a first distributor 3 for distributing an output from the amplifier 2 into two parts, a second distributor 6 for dividing an output from a phase shifter 5 which changes the phase of a reference signal output from an oscilator 4 into two parts, a first sensitive phase detector 8 for performing synchronous detection of an output of the first distributor 3 by an output of the second distributor 6 and a second sensitive phase detector 9 which performs synchronous detection of an output of the first distributor 3 by an output of a 90.degree. phase shifter 7 which causes 90.degree. phase-shift of an output of the second distributor 6 with respect to a reference signal input to the first phase detector 8.
A first A/D converter 10 and a second A/D converter 11 are provided to convert outputs of the first and second phase detectors 8, 9 into a digital form respectively. Outputs from the first and second A/D converters 10, 11 are supplied to a CPU 13 through an input circuit 15 to be stored in a memory 14, all of which constitute a computer device 12. The CPU 13 operates data stored in the memory 14 to output through an output circuit 16 to a CRT 17 which displays frequency spectrum.
FIG. 2 is a flow chart showing a program for forming frequency spectrum stored in the memory 14 of a computer device 12.
First of all, an echo signal is input to the first and second A/D converters 10, 11, where it is converted in a digital form. The digital signals are input into the input circuit 15 to start a signal inputting step 21. Upon receiving the signals from the input circuit 15, data to be processed S.sub.c (t) and S.sub.s (t) are prepared in a data preparation step 22. EQU S.sub.c (t)={Output of first A/D converter (10)}0.ltoreq.t.ltoreq.tf EQU S.sub.s (t)={Output of second A/D converter (11)}0.ltoreq.t.ltoreq.tf
Where t=0 is a starting time of A/D conversion of the echo signal; t=tf is a finishing time of A/D conversion of the echo signal in which it is assumed that the neighborhood of the center of the echo signal is subjected to the A/D conversion at t=0 and the echo signal is too small to be subjected to the A/D conversion at t=tf.
The S.sub.c (t) and S.sub.s (t) can be expressed as described below if there is a 90.degree. shift in phase between the reference signals of the first and second sensitive phase detectors 8, 9 and gain and characteristic of the detectors are same. ##EQU1##
Where A is the magnitude of outputs from the first and second sensitive phase detectors 8, 9; f(.OMEGA.) is spectrum of an angular frequency .OMEGA. to be seeked; t.sub.0 is deviation of time from the center of the echo signal to the first point of the same having been subjected to actual A/D conversion and t'+O is an error by other causes.
Assuming that there is ##EQU2## without any error. Then, t.sub.0 =0 and t'.OMEGA.+O=0 and accordingly, the following equation can be given. ##EQU3##
F(.OMEGA.) and S(t) can be obtained by an inverse Fourier transformation. Real parts and imaginary parts of S.sub.c (t) and S.sub.s (t) are subjected to the inverse Fourier transformation in a data conversion step 23 to obtain h(.OMEGA.) as follows. ##EQU4##
When a real part of h(.OMEGA.) is taken, there remains f(.OMEGA.), which is expressed by: EQU f(.OMEGA.)=the real part of {h(.OMEGA.)}
In the conventional method, frequency spectrum is obtained by using the related equation.
When there is an error, the following expression can be made; ##EQU5##
Accordingly, f(.OMEGA.) and S(t) can be obtained by using an inverse Fourier transformation. Real parts and imaginary parts of S.sub.c (t) and S.sub.s (t) are subjected to the inverse Fourier transformation in the data conversion step 23 to obtain g(.OMEGA.).
When we put ##EQU6## then, the following equations are obtainable. ##EQU7##
Since g(.OMEGA.) obtained in the data conversion step 23 includes an error in the equations, a coefficient e.sup.-i{O+.OMEGA.(t.sbsp.0.sup.+t')} contained in the g(.OMEGA.) should be eliminated. In the date processing step 24, the product of g(.OMEGA.) and e.sup.i{O+.OMEGA.(t.sbsp.0.sup.+t')} is given on the assumption of the value of O+.OMEGA.(t.sub.0 +t'). Then, the formula of ##EQU8## is obtained. Since a result obtained in the data processing step 24 is not provided as frequency spectrum, the result of the data processing step 24 is supplied to a calibration step 26 through a discrimination step 25, where calibration is carried out to make the item of ##EQU9## to be 0. The calibration in the calibration step 26 is not carried out based on any analysis but is carried out by a funtion obtained by experience. A frequency spectrum is obtained in the calibration step 26 and the real part of h(.OMEGA.) is taken in the course of from the discrimination step 25 to a spectrum outputting step 27; thus a spectrum f(.OMEGA.) is obtained. The spectrum obtained in the spectrum outputting step 27 is output to the CRT 17 through the output circuit 16 for a spectrum display step 28.
In the conventional method of calibration of error as above-mentioned, both values O and t.sub.0 +t' are assumed and a finally remaining error is calibrated based on experience. Accordingly, there were disadvantageous such that a function for calibrating the error is artificially given and the echo signal can be utilized for only half portion when a signal processing unit was designed.